# Advanced Microeconomics/Homogeneous and Homothetic Functions

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## Homogeneous & Homothetic Functions[edit]

For any scalar a function is *homogenous* if A *homothetic* function is a monotonic transformation of a homogeneous function, if there is a monotonic transformation and a homogenous function such that f can be expressed as

- A function is
*monotone*where - Assumption of homotheticity simplifies computation,
- Derived functions have homogeneous properties, doubling prices and income doesn't change demand, demand functions are homogenous of degree 0
- The slope of the MRS is the same along rays through the origin

### Example:[edit]